1. Field of the Invention
This invention is related generally to oilfield equipment for monitoring and controlling wells that are produced by rod pumping where subsurface fluid pumps are driven via a rod string which is reciprocated by a pumping unit located at the surface.
In particular, the invention concerns methods for measuring the leakage rate of the downhole pump using either measured axial load information from the drive rod string or using measured production data. The invention also concerns methods for applying that leakage rate to a downhole dynamometer card (for reciprocating rod pumps) for determining well production.
2. Description of the Prior Art
Traditional Production Testing
Knowledge of fluid production from individual wells is crucial to commercial oil and gas production. At a minimum, such knowledge facilitates accurate royalty payment, proper regulatory reporting, and improved operational decisions.
However, oil wells typically produce mixtures of oil, water, and gas. Designing and maintaining facilities to separate and measure these mixtures for each well is typically cost-prohibitive. One commonly employed alternative is to utilize “satellite” facilities with a dedicated test fixture. The production from a collection of wells is routed to a single separation and storage facility. The aggregate production from these wells is metered on a daily basis through “sales” meters. The facility is also equipped with a separate metering (“test”) system. The production from a single well is routed through this test facility for a period of time thereby allowing a “spot” measurement of the well's production. Production from each well is regularly rotated through the “test” metering system over a given period of time. At the end of a pre-determined period (often, monthly) an accounting procedure is used to allocate the aggregate production to individual wells. The allocation is performed using the “spot”/“test” measurements as a means of determining each well's individual share of the total production.
The production test method described above is far from ideal. The test metering systems are expensive to construct and to maintain. Various practical operational factors can cause the individual well “tests” to be inaccurate. Furthermore, the method does not account for transient events which occur throughout the aggregate metering period (e.g. a month) at individual wells.
Even with such traditional production testing, it may not be feasible to meet regulatory requirements. In some municipalities, the regulatory agency specifies a test frequency and a test duration such that there is insufficient time to rotate all wells from a particular “satellite” through the “test” fixture in the prescribed time.
Pump Metering
In an effort to deliver a near-continuous individual well production measurement, various efforts have been made to use the downhole pump as a meter. The initial premise of these efforts is that reciprocating rod pumps (RRP's) are generally classified as “positive displacement” pumps. For a specific amount of reciprocating travel (or “stroke”), a particular RRP should pump a specific volume of fluid. The “positive displacement meter” concept, though, is not purely applicable to oilfield downhole pumps.
U.S. Pat. No. 7,212,923 (assigned to the assignee of this application) describes a prior method of estimating production of a well from analysis of a pump card. Such patent is incorporated herein by reference as if it were exactly reproduced herein. The patent describes a well manager algorithm to be performed to obtain an estimate of liquid production passing through the pump in an interval of time. The well manager derives the liquid stroke Sl from the pump card and computes the liquid volume raised during the stroke with information as to the volume capacity of the cylinder of the pump. The well manager accumulates the liquid volumes during pumping strokes, whatever the fillage. The well manager has information as to when the pumping unit is stopped and no fluid is passing through the pump. The well manager controls when the unit runs and when it is stopped.
When 24 hours have passed, the well manager computes the inferred daily production rate, RIP, in barrels per day from the elapsed time and accumulated volumes. The inferred production, based on the geometry of the pump and the daily percentage of time the pump is in operation is understood to not reflect actual conditions of pump leakage, unanchored tubing, free gas volume in pump at time of traveling valve (TV) opening, and oil shrinkage.
Prior art methods have used a “k” factor to account for differences between measured production and inferred production using the pump as a meter. In other words:Rt=kRIP 
where Rt is the calculated daily production rate, and RIP is the unadjusted inferred daily liquid rate. Ideally, the k factor is just below 1.0, for example in the range of 0.85 to 0.9. The k factor accounts for the fact that the assumptions about actual conditions mentioned above are not always correct. According to U.S. Pat. No. 7,212,923,                (a) all pumps leak, at least slightly,        (b) tubing is not always anchored at or near the pump,        (c) a small volume of free gas is often present in the pump at the instant of traveling valve opening, and        (d) most oil shrinks as gas leaves it while passing up the tubing to the stock tank.        
Ideally, the combined total of the effects mentioned above is small, such that the “k” factor is slightly less than 0.9.
Correcting Volume at Different Pressures and Temperatures
As mentioned, oil wells typically produce a mixture of oil, water, and gas. At downhole pressures and temperatures, these mixtures can exist in nearly pure gas phase, or nearly pure liquid phase. Typically, however, the fluid at down-hole pump conditions is a mixture of liquid and gas phases. When the fluid is brought to the surface and processed, more gas is extracted and the liquid volume decreases. This result is referred to as “shrinkage.”
Oil operators traditionally measure fluid at surface pressure and temperature conditions. Yet pump metering techniques can only measure volumes at down-hole pump conditions. Therefore in order to provide an adequate replacement for surface volume measurement, any practical pump metering system should compensate for fluid density changes that result from pressure and temperature changes. Mathematical relationships used to correct between volumes measured at varying temperatures and pressures are commonly available in the industry.
Determination of Net Stroke from Pump Card
Typical reciprocating rod pump (RRP) installations rely on a pumping unit to reciprocate a long string of rods from the surface. The pump is located in the well at distances ranging from hundreds of feet to several thousand feet from the surface. Mathematical models are applied to the surface measurements of rod displacement and force to model the rod displacement and force at the downhole end of the rod string. The resulting downhole dynamometer or “pump card” represents the expected motion and load of the pump plunger.
Estimation of gross liquid production from the pump can be performed by considering the motion of the moving plunger relative to the standing valve. It is traditional to consider that the standing valve is attached to the tubing string. As fluid load is transferred between the plunger and the tubing, the long rod from the downhole pump to the surface expands and contracts. Those downhole “pump” motions, characterized by a load (force) versus plunger position graph for downhole conditions, can be very different from the surface dynamometer, or rod force versus rod position graph at the surface. The prior art applies mathematical models to surface measurements of force and displacement of the rod string, in order to estimate downhole force and displacement of the pump, that is, the pump card.
Estimation of net pump stroke requires detailed interpretation of the pump card. See FIG. 1 which shows a pump card. The opening and closing positions of both the standing and the traveling valve must be identified. The fluid load lines must also be identified. The existence of the fluid load lines is a direct result of the opening and closing of the standing and traveling valves.
An ideal pump card demonstrates a stable load (FLus) during most of the upstroke and a different stable load (FLds) during most of the downstroke. See the load lines FLus and FLds on FIG. 1. The stabilized pump load during the downstroke (FLds) should correspond to the buoyant force on the bottom of the rod string, if the pump card were generated using “true loads”. If the pump card were generated using “effective loads,” FLds should be at zero pounds force. On the upstroke, the stabilized load (FLus) should be offset from the downstroke stabilized fluid (FLds) by an amount equal to the cross-sectional area of the pump multiplied by the pressure difference across the pump plunger.
The standing valve is the appropriate reference point for measuring production through the pump. FIG. 1 depicts an idealized “full” card for the general case. The offset in plunger position between closing of the traveling valve TVC and opening of the standing valve SVO is caused by a number of factors. First, there is an amount of plunger movement which must occur to counteract tubing contraction. As the traveling valve, plunger and rod string begin to take on the fluid load, the tension on the bottom end of the tubing decreases. This allows the tubing string to contract. During the transition from TVC to SVO, the pressure differential across the plunger is increasing. Any time there is a pressure difference across the plunger, there will be some leakage. Before the standing valve can open, the traveling valve must move enough distance to not only offset the tubing contraction (St), but also offset the amount of liquid which has leaked around the plunger during the early portion of the upstroke (Sleakage (TVC˜SVO)). Other factors, such as delayed traveling valve sealing caused by a “tight” ball catcher, can also add to the offset in position between TVC and SVO (Sother). See FIG. 1.
U.S. Pat. No. 7,212,923 describes a procedure that accounts for the offset between TVC and SVO using only a calculated estimate of tubing contraction (St). When an estimation of Sleakage is not applied to actual field data, the result is over-estimation of the net pump stroke, because the total offset in position between TVC and SVO exceeds that predicted by the tubing contraction St calculation.
Compensating for Pump Leakage (Slippage)
RRP's operate at very high pressures (hundreds to thousands of pounds force per square inch) in downhole conditions. These pumps are often intentionally designed to allow a certain amount of fluid to leak through the primary pump seals. This leakage is sometimes called “slip”. In order to use the pump as a meter, the amount of “slippage” must be accurately determined.
In the technical field of RRP's, several investigators have attempted to mathematically model the slippage through a RRP using known characteristics of the pump and of the fluid being pumped. A published Master's Thesis by Richard Chambliss in 2001 provides a good review of these efforts. As Chambliss pointed out, attempts to experimentally validate these mathematical models have been troublesome, at best. Even under laboratory conditions where all of the parameters entered into the model are known, there is still a considerable amount of uncertainty in the results. In actual field conditions, however, even the parameters input into the mathematical models (pump clearance, fluid viscosity, plunger-barrel eccentricity) are not known. Therefore practitioners in the industry cannot rely on any of these models as a means to correct positive displacement pump meters for slip.
Gibbs and Nolen in an August 1990 article in the publication, SPE Production Engineering, proposed a series of methods for measuring pump leakage (slip) “in situ” for a single stroke of an RRP. These practical field procedures (and adaptations of those techniques) have been employed with varying degrees of success for more than two decades. More recently, Gibbs and Nolen proposed in U.S. Pat. No. 7,212,923 using these techniques in a wellsite controller to continuously infer production from a RRP system.
Gibbs and Nolen proposed several alternative approaches for estimating RRP slippage. They suggested that their “Pump Card Method” (“923” patent, column 10, line 40) is more applicable to “severely worn” pumps. Presumably this means pumps with high slippage.
They described another (“Traveling Valve Load Loss Rate”) (“923” patent, column 12, line 35) method using the phrase “works well in all cases as long as the load loss trace is not nearly vertical.”
A third alternative method (“rolling stop” method) was suggested in cases where the “Traveling Valve Load Loss Rate” is not appropriate.
Gibbs and Nolen therefore, suggest that an automatic well controller device when used to estimate production may implement one of three separate slippage estimation techniques. No direction is provided as to how to select which one of the three methods to use for an actual pumping well in an oilfield.
The “Pump card method” has proven difficult to implement even when a human attempts to interpret the data. The “Pump card method” involves subtle interpretation of the derivative of the pump card data. Downhole pump cards are the result of a complex chain of calculations derived from raw data which includes a degree of error or noise. The result is that downhole cards can be “noisy” and tend to have fairly low resolution in time. When these low resolution, “noisy” data are differentiated in an attempt to apply the “Pump card Method”, the “noise” is dramatically amplified. As a result, the “standard valve opening” (SVO) time is difficult (sometimes impossible) for even a human to identify. Logic designed for a controller to interpret this data, almost certainly results in frequent erroneous selection of “standing valve opening” time, thereby yielding incorrect estimates of pump leakage. Therefore, the Gibbs and Nolen “Pump Card method” does not provide a generally useful method of estimating pump leakage across a broad range of oilfield installations.
The Gibbs and Nolen “Traveling Valve Load Loss Rate” method is the most commonly utilized leakage estimation procedure in the industry. This method involves stopping the RRP system during the “upstroke” when the load of the produced fluid column is carried by the RRP traveling valve. (See TVC of FIG. 1). The axial tension (load) of the drive string is measured after motion is stopped. Gibbs and Nolen relate the load loss rate to strain in the rod and tubing strings. This strain is then considered to result in downhole pump plunger movement. Gibbs and Nolen proposed a procedure for interpreting this data which involves selecting three points on the load decline curve. A second order polynomial (parabola) is forced to fit these three points, and the equation of the parabola is differentiated to obtain a load loss rate (lbf/sec). The load loss rate is then converted to a strain rate in inches/sec using elasticity and cross-sectional area of the rod string and any unanchored tubing. Gibbs and Nolen then apply this strain rate to the cross-sectional area of the pump to determine an associated pump displacement rate in BPD.
According to Gibbs and Nolen, this procedure results in an estimate of maximum leakage rate (in BPD) which can be applied using a “leaking coefficient” (Cp) thereby providing a total leakage determination.
Although the Gibbs and Nolen “Traveling Valve Load Loss Rate” method and variants of the technique have been widely used throughout the industry for many years, no literature can be found which challenges or confirms the validity of the “Traveling Valve Load Loss Rate” procedure.
A review of the Nolen, Gibbs paper of SPE Production Engineering, August 1990, and U.S. Pat. No. 7,212,923 of Gibbs identifies a number of shortcomings of this technique.
Time-Dependent Leakage
The “Traveling Valve Load Loss Rate” technique includes an interpretation procedure which relies on the polished rod load vs time data. Gibbs and Nolen did not provide any theoretical basis for assuming a relationship between leakage rate and time.
Second Order Approximation
In the August 1990 paper of Nolen, Gibbs, equations are presented which can be used to fit a second order equation (parabola) through three points selected by an analyst from the polished rod load vs time data. Nolen and Gibbs presented no theoretical or other argument to support the use of a second order approximation of the (load vs time) data. In fact, the figures described below illustrate how poorly the second order equation approximates the entire load decline curve.
FIG. 2 is a graph of raw load decline data from an actual “traveling valve check”.
FIGS. 3, 4 and 5 depict this same data along with the Nolen, Gibbs second order approximation curve. In each case, a different set of three points was selected for the curve fit.
In all three cases, the second order equation does a very poor job of approximating the entire raw data set.
Highly Subjective Interpretation
Nolen-GibbsNolen-GibbsFIG.k1 [Ibf/sec]Leakage [BPD]3−28027.54−23122.75−39535.3FIGS. 3 through 5 illustrate the subjectivity of “Traveling Valve Load Loss Rate” interpretation. Simply by moving the selected points to different locations on the load decline curve, the calculated leakage can vary dramatically. In the three cases displayed, the leakage rates were calculated to be 27.5, 22.7, and 35.3 BPD, respectively (representing up to 24% deviation from the mean value). Such variability in leakage estimates is highly undesirable.Incompressible Fluid Assumption
In relating polished rod load loss to leakage rate (via plunger movement), the Gibbs and Nolen model (without explicitly stating) is based on several assumptions:
Pump plunger expansion due to internal-external pressure difference is negligible;
Pump barrel expansion due to internal-external pressure difference is negligible; and
Fluid inside the barrel is incompressible.
The first two assumptions are generally valid, because engineering calculations show that plunger and barrel expansions are very small.
However, operational conditions can easily invalidate the assumption of incompressible fluid. If the fluid entering the pump has any free gas content or if the barrel is incompletely filled at the time that the polished rod is stopped for a traveling valve test, the fluid in the pump barrel will be highly compressible. In these cases, the correlations between plunger movement and leakage rate assumed by Gibbs and Nolen are invalid.
The Gibbs and Nolen “Traveling Valve Load Loss Rate” method calculates fluid leakage as being equal to the plunger movement (attributable to the contraction of the rod string due to load loss) times the plunger cross-sectional area. However, critical analysis reveals that for a system containing a compressible fluid, the actual leakage rate is that calculated by Gibbs and Nolen plus enough fluid to compensate for the compression of the liquid already in the barrel to its new, elevated pressure.
Problems with fluid compressibility are most serious during the very early parts of the traveling valve leakage test, where the pressure in the barrel is lowest. However, this is also the portion of the data which is most crucial to the Gibbs and Nolen interpretation. Therefore, the fluid compressibility phenomena can introduce significant error into the leakage calculations.
If the pump barrel contains compressible fluid, actual leakage rates will be significantly higher than those calculated by the Gibbs and Nolen “Traveling Valve Load Loss Rate” technique.